Sự Xuất Hiện Của Tỷ Lệ Tăng Trưởng Trong Các Mạng Ngẫu Nhiên
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; R. F. Service ibid. p. 80.
G. Weng U. S. Bhalla R. Iyengar ibid. p. 92.
C. Koch and G. Laurent ibid. p. 96.
; see also .
P. Erdős and
Rényi A., Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960);
; B. Bollobás Random Graphs (Academic Press London 1985).
In addition to the distribution of incoming links the WWW displays a number of other scale-free features characterizing the organization of the Web pages within a domain [
] the distribution of searches [
] or the number of links per Web page (6).
We also studied the neural network of the worm Caenorhabditis elegans (3 10) and the benchmark diagram of a computer chip (see ). We found that P(k) for both was consistent with power-law tails despite the fact that for C. elegans the relatively small size of the system (306 vertices) severely limits the data quality whereas for the wiring diagram of the chips vertices with over 200 edges have been eliminated from the database.
Milgram S., Psychol. Today 2, 60 (1967);
; M. Kochen ed. The Small World (Ablex Norwood NJ 1989).
J. Guare Six Degrees of Separation: A Play (Vintage Books New York 1990).
Barthélémy M., Amaral L. A. N., Phys. Rev. Lett. 82, 15 (1999).
For most networks the connectivity m of the newly added vertices is not constant. However choosing m randomly will not change the exponent γ (Y. Tu personal communication).
Preferential attachment was also used to model evolving networks (L. A. N. Amaral and M. Barthélémy personal communication).
We thank D. J. Watts for providing the C. elegans and power grid data B. C. Tjaden for supplying the actor data H. Jeong for collecting the data on the WWW and L. A. N. Amaral for helpful discussions. This work was partially supported by NSF Career Award DMR-9710998.